The Bessel function of order 1 is (a) Show that the series converges for all x (b) Show that the series is a solution of the differential equation (c) Use a graphing utility to graph the polynomial composed of the first four terms of J 1 (d) Use J 0 from Exercise 65 to show that J 0 '(x) J 1 (x) Use J 0 from Exercise 65 The Bessel function of order 0 is ( 1) xk J(x) x 22k k (k 1) k 0

Question: The Bessel function of order 1 is (a) Show that the series converges for all x. (b) Show that the series is a solution of

The Bessel function of order 1 is

(-1)*.xk J(x) = x 22k+k!(k + 1)! k=0

(a) Show that the series converges for all x.

(b) Show that the series is a solution of the differential equation

(d) Use J₀ from Exercise 65 to show that J₀'(x) = -J₁(x).

Use J₀ from Exercise 65

The Bessel function of order 0 is

(-1)*.xk J(x) = x 22k+k!(k + 1)! k=0

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